This invention relates to the encipherment of binary and non-binary digital sequences such as used in communications by reversible transposition methods and the decipherment of sequences enciphered by reversible transposition methods. More specifically it relates to applying methods using recoded binary and non-binary pseudo-noise sequences generated by LFSR based sequence generators and other methods that will generate reversible sequences.
Sequences comprised of digital elements have known applications in communications and other applications. In general binary pseudo-noise or PN-sequences are used. Application of non-binary sequences is also possible. Linear feedback shift register (LFSR) circuits or methods are often used for the generation and detection of sequences. LFSR circuits with p register elements can generate (np−1) length unique n-valued sequences which are called maximum-length sequences. It is often desirable to encrypt digital data for transmission, or storage on a data-storage medium such as optical disks or as an embedded message for watermarking applications.
Substitution ciphers are known, wherein according to some rules one symbol or series of symbols is replaced by another. Another encipherment method is transposition wherein in a series of symbols the order of the symbols is changed according to a rule or set of rules.
While transposition encipherment can be used for security reasons, it can also be used to randomize a process in a recoverable way. One such application is the creation of sequences for application in frequency hopping in telecommunications. In many cases binary LFSR based pseudo-random sequences are used as a number generator to create hopping rules. Orthogonality of the sequences is important so that each user in a hop is assigned a unique frequency slot. Another application is in time-hopping applications. Herein each user is assigned a unique time-slot, so that pulses of different users do not collide. Non-binary pseudo-random sequences have statistical advantages over the generally used binary sequences. It is often useful to have a local method to generate the transposition rule as well as the rule to recover the transposed sequence. Also the ability to select from a large number of possible encipherment rules is advantageous.
Accordingly, new methods for symbol transposition in a pseudo-random like fashion are required.